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4 years ago

What is the area of a rectangle with vertices at (−3, −1) , (1, 3) , (3, 1) , and (−1, −3) ?

1 answer:

8 0

16 square units. Let's use the pythagorean theorem to determine the lengths of each side of the rectangle. A = (-3,-1), B = (1,3), C = (3,1), D = (-1,-3) Length AB^2 = (-3 - 1)^2 + (-1 -3)^2 = -4^2 + -4^2 = 16+16 = 32 Length BC^2 = (1 - 3)^2 + (3-1)^2 = -2^2 + 2^2 = 4 + 4 = 8 Length CD^2 = (3-(-1))^2 + (1-(-3))^2 = 4^2 + 4^2 = 16+16 = 32 Length AD^2 = (-3 - (-1))^2 + (-1 - (-3))^2 = -2^2 + 2^2 = 4 + 4 = 8 And just to make certain I haven't accidentally included the diagonal of the rectangle, I'll check AC and BD. So Length AC^2 = (-3 - 3)^2 + (-1 - 1)^2 = -6^2 + -2^2 = 36 + 4 = 40 Length BD^2 = (1 - (-1))^2 + (3 - (-3))^2 = 2^2 + 6^2 = 4 + 36 = 40 So I now know that length of the rectangle is sqrt(32) and the width is sqrt(8). And the area will be the product of those 2 numbers. So sqrt(32)*sqrt(8) = sqrt(256) = 16. So the area of the rectangle is 16 square units.

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Answer:Lewis Cass (October 9, 1782 – June 17, 1866) was an American military officer, politician, and statesman. He represented Michigan in the United States Senate and served in the Cabinets of two U.S. Presidents, Andrew Jackson and James Buchanan. He was also the 1848 Democratic presidential nominee and a leading spokesman for the Doctrine of Popular Sovereignty, which held that the people in each territory should decide whether to permit slavery.

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Contents

1 Early life

2 Career

2.1 War of 1812

2.2 Territorial Governor of Michigan

2.3 Secretary of War

2.4 U.S. Minister to France

2.5 Presidential ambitions and U.S. Senate

2.6 U.S. Secretary of State

3 Personal life

3.1 Descendants

4 Commemoration

5 Other honors and memberships

6 Publications

7 See also

8 References

9 Bibliography

10 External links

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